Abstract

We developed an importance sampling based method that significantly speeds up the calculation of the diffusive reflectance due to ballistic and to quasi-ballistic components of photons scattered in turbid media: Class I diffusive reflectance. These components of scattered photons make up the signal in optical coherence tomography (OCT) imaging. We show that the use of this method reduces the computation time of this diffusive reflectance in time-domain OCT by up to three orders of magnitude when compared with standard Monte Carlo simulation. Our method does not produce a systematic bias in the statistical result that is typically observed in existing methods to speed up Monte Carlo simulations of light transport in tissue. This fast Monte Carlo calculation of the Class I diffusive reflectance can be used as a tool to further study the physical process governing OCT signals, e.g., obtain the statistics of the depth-scan, including the effects of multiple scattering of light, in OCT. This is an important prerequisite to future research to increase penetration depth and to improve image extraction in OCT.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
    [CrossRef]
  2. C. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, and S. A. Boppart, “Spectroscopic spectral-domain optical coherence microscopy,” Opt. Lett. 31(8), 1079–1081 (2006).
    [CrossRef] [PubMed]
  3. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
    [CrossRef] [PubMed]
  4. B. Liu and M. E. Brezinski, “Theoretical and practical considerations on detection performance of time domain, Fourier domain, and swept source optical coherence tomography,” J. Biomed. Opt. 12(4), 044007 (2007).
    [CrossRef] [PubMed]
  5. G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44(9), 2307–2320 (1999).
    [CrossRef] [PubMed]
  6. S. S. Sherif, C. C. Rosa, C. Flueraru, S. Chang, Y. Mao, and A. G. Podoleanu, “Statistics of the depth-scan photocurrent in time-domain optical coherence tomography,” J. Opt. Soc. Am. A 25(1), 16–20 (2008).
    [CrossRef] [PubMed]
  7. M. J. Yadlowsky, J. M. Schmitt, and R. F. Bonner, “Multiple scattering in optical coherence microscopy,” Appl. Opt. 34(25), 5699–5707 (1995).
    [CrossRef] [PubMed]
  8. B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
    [CrossRef] [PubMed]
  9. L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
    [CrossRef] [PubMed]
  10. N. G. Chen and J. Bai, “Estimation of quasi-straightforward propagating light in tissues,” Phys. Med. Biol. 44(7), 1669–1676 (1999).
    [CrossRef] [PubMed]
  11. N. Chen, “Controlled Monte Carlo method for light propagation in tissue of semi-infinite geometry,” Appl. Opt. 46(10), 1597–1603 (2007).
    [CrossRef] [PubMed]
  12. R. Y. Rubinstein, Simulation and the Monte Carlo Method (Wiley, 1981).
  13. G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(3), 310–312 (2002).
    [CrossRef]
  14. S. L. Fogal, G. Biondini, and W. L. Kath, “Multiple importance sampling for first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(9), 1273–1275 (2002).
    [CrossRef]
  15. I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett. 15(1), 45–47 (2003).
    [CrossRef]
  16. I. T. Lima, A. O. Lima, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol. 22(4), 1023–1032 (2004).
    [CrossRef]
  17. J. M. Schmitt and K. Ben-Letaief, “Efficient Monte Carlo simulation of confocal microscopy in biological tissue,” J. Opt. Soc. Am. A 13(5), 952–961 (1996).
    [CrossRef] [PubMed]
  18. H. Iwabuchi, ““Efficient Monte Carlo method for radiative transfer modeling,” J. of the Atmosph,” Science 63, 2324–2339 (2006).
  19. I. T. Lima, Jr., “Advanced Monte Carlo methods applied to Optical Coherence Tomography” (invited), presented at the 2009 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, Belém, Brazil, 3–6 Nov. 2009.
  20. “Monte Carlo simulations,” Oregon Medical Laser Center, accessed January 1, 2009, http://omlc.ogi.edu/software/mc/
  21. S. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (Prentice-Hall, 1993).
  22. E. Hecht, Optics, 4th ed. (Pearson Addison Wesley, 2003).

2008 (1)

2007 (2)

N. Chen, “Controlled Monte Carlo method for light propagation in tissue of semi-infinite geometry,” Appl. Opt. 46(10), 1597–1603 (2007).
[CrossRef] [PubMed]

B. Liu and M. E. Brezinski, “Theoretical and practical considerations on detection performance of time domain, Fourier domain, and swept source optical coherence tomography,” J. Biomed. Opt. 12(4), 044007 (2007).
[CrossRef] [PubMed]

2006 (2)

C. Xu, C. Vinegoni, T. S. Ralston, W. Luo, W. Tan, and S. A. Boppart, “Spectroscopic spectral-domain optical coherence microscopy,” Opt. Lett. 31(8), 1079–1081 (2006).
[CrossRef] [PubMed]

H. Iwabuchi, ““Efficient Monte Carlo method for radiative transfer modeling,” J. of the Atmosph,” Science 63, 2324–2339 (2006).

2004 (1)

2003 (3)

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
[CrossRef] [PubMed]

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett. 15(1), 45–47 (2003).
[CrossRef]

2002 (2)

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(3), 310–312 (2002).
[CrossRef]

S. L. Fogal, G. Biondini, and W. L. Kath, “Multiple importance sampling for first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(9), 1273–1275 (2002).
[CrossRef]

1999 (2)

N. G. Chen and J. Bai, “Estimation of quasi-straightforward propagating light in tissues,” Phys. Med. Biol. 44(7), 1669–1676 (1999).
[CrossRef] [PubMed]

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44(9), 2307–2320 (1999).
[CrossRef] [PubMed]

1996 (1)

1995 (2)

M. J. Yadlowsky, J. M. Schmitt, and R. F. Bonner, “Multiple scattering in optical coherence microscopy,” Appl. Opt. 34(25), 5699–5707 (1995).
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

1983 (1)

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Adam, G.

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Bai, J.

N. G. Chen and J. Bai, “Estimation of quasi-straightforward propagating light in tissues,” Phys. Med. Biol. 44(7), 1669–1676 (1999).
[CrossRef] [PubMed]

Ben-Letaief, K.

Biondini, G.

I. T. Lima, A. O. Lima, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol. 22(4), 1023–1032 (2004).
[CrossRef]

S. L. Fogal, G. Biondini, and W. L. Kath, “Multiple importance sampling for first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(9), 1273–1275 (2002).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(3), 310–312 (2002).
[CrossRef]

Bonner, R. F.

Boppart, S. A.

Brezinski, M. E.

B. Liu and M. E. Brezinski, “Theoretical and practical considerations on detection performance of time domain, Fourier domain, and swept source optical coherence tomography,” J. Biomed. Opt. 12(4), 044007 (2007).
[CrossRef] [PubMed]

Chang, S.

Chen, N.

Chen, N. G.

N. G. Chen and J. Bai, “Estimation of quasi-straightforward propagating light in tissues,” Phys. Med. Biol. 44(7), 1669–1676 (1999).
[CrossRef] [PubMed]

Choma, M.

Drexler, W.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Fercher, A. F.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Flueraru, C.

Fogal, S. L.

S. L. Fogal, G. Biondini, and W. L. Kath, “Multiple importance sampling for first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(9), 1273–1275 (2002).
[CrossRef]

Hitzenberger, C. K.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Iwabuchi, H.

H. Iwabuchi, ““Efficient Monte Carlo method for radiative transfer modeling,” J. of the Atmosph,” Science 63, 2324–2339 (2006).

Izatt, J.

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

Kath, W. L.

I. T. Lima, A. O. Lima, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol. 22(4), 1023–1032 (2004).
[CrossRef]

S. L. Fogal, G. Biondini, and W. L. Kath, “Multiple importance sampling for first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(9), 1273–1275 (2002).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(3), 310–312 (2002).
[CrossRef]

Lasser, T.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Lima, A. O.

I. T. Lima, A. O. Lima, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol. 22(4), 1023–1032 (2004).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett. 15(1), 45–47 (2003).
[CrossRef]

Lima, I. T.

I. T. Lima, A. O. Lima, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol. 22(4), 1023–1032 (2004).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett. 15(1), 45–47 (2003).
[CrossRef]

Liu, B.

B. Liu and M. E. Brezinski, “Theoretical and practical considerations on detection performance of time domain, Fourier domain, and swept source optical coherence tomography,” J. Biomed. Opt. 12(4), 044007 (2007).
[CrossRef] [PubMed]

Luo, W.

Mao, Y.

Menyuk, C. R.

I. T. Lima, A. O. Lima, G. Biondini, C. R. Menyuk, and W. L. Kath, “A comparative study of single section polarization-mode dispersion compensators,” J. Lightwave Technol. 22(4), 1023–1032 (2004).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett. 15(1), 45–47 (2003).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(3), 310–312 (2002).
[CrossRef]

Podoleanu, A. G.

Ralston, T. S.

Rosa, C. C.

Sarunic, M.

Schmitt, J. M.

Sherif, S. S.

Tan, W.

Vinegoni, C.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

Wang, L. V.

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44(9), 2307–2320 (1999).
[CrossRef] [PubMed]

Wilson, B. C.

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Xu, C.

Yadlowsky, M. J.

Yang, C.

Yao, G.

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44(9), 2307–2320 (1999).
[CrossRef] [PubMed]

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

Zweck, J.

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett. 15(1), 45–47 (2003).
[CrossRef]

Appl. Opt. (2)

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (3)

G. Biondini, W. L. Kath, and C. R. Menyuk, “Importance sampling for polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(3), 310–312 (2002).
[CrossRef]

S. L. Fogal, G. Biondini, and W. L. Kath, “Multiple importance sampling for first- and second-order polarization-mode dispersion,” IEEE Photon. Technol. Lett. 14(9), 1273–1275 (2002).
[CrossRef]

I. T. Lima, A. O. Lima, J. Zweck, and C. R. Menyuk, “Efficient computation of outage probabilities due to polarization effects in a WDM system using a reduced Stokes model and importance sampling,” IEEE Photon. Technol. Lett. 15(1), 45–47 (2003).
[CrossRef]

J. Biomed. Opt. (1)

B. Liu and M. E. Brezinski, “Theoretical and practical considerations on detection performance of time domain, Fourier domain, and swept source optical coherence tomography,” J. Biomed. Opt. 12(4), 044007 (2007).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

Med. Phys. (1)

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (2)

N. G. Chen and J. Bai, “Estimation of quasi-straightforward propagating light in tissues,” Phys. Med. Biol. 44(7), 1669–1676 (1999).
[CrossRef] [PubMed]

G. Yao and L. V. Wang, “Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,” Phys. Med. Biol. 44(9), 2307–2320 (1999).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003).
[CrossRef]

Science (1)

H. Iwabuchi, ““Efficient Monte Carlo method for radiative transfer modeling,” J. of the Atmosph,” Science 63, 2324–2339 (2006).

Other (5)

I. T. Lima, Jr., “Advanced Monte Carlo methods applied to Optical Coherence Tomography” (invited), presented at the 2009 SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference, Belém, Brazil, 3–6 Nov. 2009.

“Monte Carlo simulations,” Oregon Medical Laser Center, accessed January 1, 2009, http://omlc.ogi.edu/software/mc/

S. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (Prentice-Hall, 1993).

E. Hecht, Optics, 4th ed. (Pearson Addison Wesley, 2003).

R. Y. Rubinstein, Simulation and the Monte Carlo Method (Wiley, 1981).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic representation of the vectors and the angles used in the bias procedure.

Fig. 2
Fig. 2

Schematic representation of a simulation setup similar to [5].

Fig. 3
Fig. 3

The Class I diffuse reflectance as a function of the depth for the first simulation setup described in Sec. 4, whose schematic representation is shown in Fig. 2. The black solid line are results obtained with 2 × 106 Monte Carlo simulations with the importance sampling method described in Sec. 4. The green long-dashed line are results obtained with 1010 standard Monte Carlo samples. The black double-dashed line are results obtained using the angle bias procedure described in [5]. The pink short-dashed lines are results of plus and minus one standard deviation of Monte Carlo simulations with importance sampling with 2 × 106 samples that were estimated using an ensemble with 64 × 106 simulations.

Fig. 4
Fig. 4

The same Class I diffuse reflectance results shown in Fig. 3, except that the Class I diffuse reflectance is shown in linear scale for the depth interval from 310 µm to 380 µm. The error bars shown for the solid and for the dashed line were estimated in each respective Monte Carlo simulation.

Fig. 5
Fig. 5

The number of Class I photon packets diffusely reflected as a function of the depth in the simulations whose results are shown in Fig. 3. The black solid line are results obtained with 2 × 106 Monte Carlo simulations with the importance sampling method described in Sec. 3. The green long-dashed line are results obtained with 1010 standard Monte Carlo simulations. The pink short-dashed line are results obtained with 107 previously implemented Monte Carlo method samples.

Fig. 6
Fig. 6

Schematic representation of a simulation setup with multiple layers with different refractive indices.

Fig. 7
Fig. 7

The Class I diffuse reflectance as a function of the distance from the center of the optical fiber for the second simulation setup described in Sec. 4, whose schematic representation is shown in Fig. 6. The black solid line are results obtained with 2 × 105 Monte Carlo simulations with the importance sampling method described in Sec. 4. The green long-dashed line are results obtained with 109 standard Monte Carlo samples. The blue dots are results obtained with 106 standard Monte Carlo simulations. The pink short-dashed lines are results of plus and minus one standard deviation of Monte Carlo simulations with importance sampling with 2 × 105 samples that were estimated using an ensemble with 64 × 105 simulations.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

f H G ( cos θ s ) = 1 g 2 2 ( 1 + g 2 2 g cos θ s ) 3 / 2 ,
I 1 ( z , i ) = { 1    r i < d max ,    θ s , i < θ max ,    | Δ s i 2 z | < l c 0   otherwise,
R 1 ( z ) = 1 N i = 1 N I 1 ( z , i ) W ( i )
σ R , 1 2 ( z ) = 1 N 1 i = 1 N [ I 1 ( z , i ) W ( i ) R 1 ] 2 ,
z d , j ' = z L , j n j n j 1 ( z L , j z d , j 1 ' ) ,
v ^ = z d , j ' z ^ R .
f B ( cos θ B ) = 1 a 2 2 ( 1 + a 2 2 a cos θ B ) 3 / 2 ,
L ( cos θ B ) = f H G ( cos θ S ) f B ( cos θ B ) = 1 g 2 1 a 2 ( 1 + a 2 2 a cos θ B 1 + g 2 2 g cos θ S ) 3 / 2 ,
R 1 ( z ) = 1 N i = 1 N I 1 ( z , i ) L ( i ) W ( i )
σ R , 1 2 ( z ) = 1 N 1 i = 1 N [ I 1 ( z , i ) L ( i ) W ( i ) R 1 ] 2 .

Metrics